When you give a VM a Bridged Adapter, its affectingly like giving it its own NIC connected directly to your network.
The Ubuntu installation inside of the VM needs to be set to use a static IP address. This is done in the
/etc/network/interfaces file. Some information about the
interfaces file can be found on this page: https://help.ubuntu.com/12.04/serverguide/network-configuration.html
Here is an example
interfaces file configured to match your question:
# This file describes the network interfaces available on your system
# and how to activate them. For more information, see interfaces(5).
# The loopback network interface
iface lo inet loopback
iface eth0 inet static
After making modifications to
/etc/network/interfaces, restart your VM for the changes to take effect.